已知:cos(π6-α)=33,则sin2(α-π6)-cos(5π6+α)的值为______.-数学

题目简介

已知:cos(π6-α)=33,则sin2(α-π6)-cos(5π6+α)的值为______.-数学

题目详情

已知:cos(
π
6
-α)=
3
3
,则sin2(α-
π
6
)-cos(
6
+α)
的值为______.
题型:填空题难度:中档来源:不详

答案

sin2(α-class="stub"π
6
)=1-cos2(class="stub"π
6
-α)
=1-(
3
3
)2=class="stub"2
3
,cos(class="stub"5π
6
+α)
=cos[π-(class="stub"π
6
-α)]=-cos(class="stub"π
6
-α)=-
3
3

sin2(α-class="stub"π
6
)-cos(class="stub"5π
6
+α)
=1-cos2(class="stub"π
6
-α)
-cos(class="stub"5π
6
+α)
=1-class="stub"1
3
+
3
3
=
2+
3
3

故答案为
2+
3
3

更多内容推荐